Fermi Surface and Positron Annihilation in Sodium

The angular correlation of photons from positrons annihilating in polycrystalline sodium has been measured. The results show two things: (a) In comparison with a free-electron theory, the Fermi surface in Na is probably anisotropic by an amount of the order of 5% of $p_F$. (b) The probability of annihilation is not very velocity dependent over the range of conduction-electron velocities in Na. This is not inconsistent with the calculations of either Daniel and Friedel or of Kahana.